Lattice Boltzmann for Linear Elastic Solids
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Recent modeling frameworks to predict the mechanics of additive manufacturing processes involve both fluid and solid mechanics, with the former often described adopting the lattice Boltzmann method. Motivated by the wish to model all physics with the same method, we proposed a novel lattice Boltzmann formulation to solve the equations of linear elastic solids [1, 2]. In comparison to previous attempts in the same direction [3, 4], our approach aims at higher accuracy and efficiency, as well as at retaining the computational benefits of the lattice Boltzmann method. In this contribution we outline the construction of a novel lattice Boltzmann formulation to solve the equations of linear elasticity with second-order accuracy [1]. Hereby, it becomes apparent that the formulation of boundary conditions plays an essential role in achieving this goal. Therefore, we specifically focus on the systematic derivation of sufficiently accurate boundary formulations for Dirichlet and Neumann boundary conditions that hold for arbitrary curved domain boundaries in 2D [2]. The analytical derivation of all required expressions is guided by the asymptotic expansion technique [5] and the formulations are verified by numerical experiments using manufactured solutions. References [1] Boolakee, O., Geier, M. and De Lorenzis, L. A new lattice Boltzmann scheme for linear elastic solids: periodic problems. Comp. Meth. Appl. Mech. Eng. (2023) 404:115756. [2] Boolakee, O., Geier, M. and De Lorenzis, L. Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains. Comp. Meth. Appl. Mech. Eng. (2023) 415:116225. [3] Yin, X., Yan, G. and Li, T. Direct simulations of the linear elastic displacements field based on a lattice Boltzmann model. Int. J. Num. Meth. Eng. (2016) 107:234–251. [4] Murthy, J. S. N. et al. Lattice Boltzmann Method for Wave Propagation in Elastic Solids. Comm. Comp. Phys. (2018) 23:1223–1240. [5] Geier, M. and Pasquali, A. Fourth order Galilean invariance for the lattice Boltzmann method. Comp. Fluids (2018) 166:139–151.